Flow Measurement · Glossary

What is Square Root Extraction?

flow ∝ √DPFlow Measurement

Square root extraction converts a DP signal into a linear flow signal, because flow through a DP element is proportional to √DP.

Square Root Extraction Explained

A DP transmitter outputs a signal proportional to DP. Flow is proportional to the square root of DP, so the signal must be square rooted, either in the transmitter or in the DCS, but never in both.

Near zero the square root curve is very steep, so tiny DP errors become large flow errors. A low flow cutoff is used to stop noise showing as flow.

Square Root Extraction Formula

Q = Q_max × √(ΔP ÷ ΔP_max)

Q_max	flow at full scale DP
ΔP	measured DP
ΔP_max	calibrated DP span

Example: At 25 % of DP span the flow is 50 % of maximum; at 1 % of DP it is already 10 %.

Calculators for Square Root Extraction

CalculatorOrifice Flow CalculatorFree online calculator with formula and worked example.CalculatorDP Flow Rerange CalculatorFree online calculator with formula and worked example.

Frequently Asked Questions

What is Square Root Extraction?

Square root extraction converts a DP signal into a linear flow signal, because flow through a DP element is proportional to √DP.

Transmitter or DCS square root?

Either works. Choose one, record it on the data sheet and loop diagram, and check that the other is set to linear.

What is the 4 to 20 mA value at 50 % flow?

With square root in the DCS, 50 % flow is 25 % DP, so the transmitter sends 4 + 0.25 × 16 = 8 mA.

Learn more on the blog

Mistakes in DP flow measurement

A practical guide on instrumentationblog.in with more detail on square root extraction and how it is applied on real plants.

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